Related papers: Occupancy times for time-dependent stage-structure…

Spatio-temporal pattern formation over the square and rectangular domain has received significant attention from researchers. A wide range of stationary and non-stationary patterns produced by two interacting populations is abundant in the…

Resource are often not uniformly distributed within a population. Spatial variations of concentration of a resource, change the fitness of competing strategies locally. The notion of fitness varying with respect to both genotype and…

State-space models effectively model multivariate time series by updating over time a representation of the system state from which predictions are made. The state representation is usually a vector without any explicit structure.…

The occupation time of an age-dependent branching particle system in $\Rd$ is considered, where the initial population is a Poisson random field and the particles are subject to symmetric $\alpha$-stable migration, critical binary branching…

The time evolution of many physical, chemical, and biological systems can be modelled by stochastic transitions between the minima of the potential energy surface describing the system of interest. We show that in cases where there are two…

We propose a discrete-time, finite-state stationary process that can possess long-range dependence. Among the interesting features of this process is that each state can have different long-term dependency, i.e., the indicator sequence can…

We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…

We examine the switching dynamics of a stochastic population subjected to a deterministically time-varying environment. Our approach is demonstrated in the realm of ecology on a problem of population establishment. Here, by assuming a…

We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…

In this paper, we introduce a spatial model for dormancy in random environment via a two-type branching random walk in continuous-time, where individuals can switch between dormant and active states through spontaneous switching independent…

For autonomous vehicles to proactively plan safe trajectories and make informed decisions, they must be able to predict the future occupancy states of the local environment. However, common issues with occupancy prediction include…

We examine birth--death processes with state dependent transition probabilities and at least one absorbing boundary. In evolution, this describes selection acting on two different types in a finite population where reproductive events occur…

Many types of spatiotemporal patterns have been observed under nonequilibrium conditions. Cycling through four or more states can provide specific dynamics, such as the spatial coexistence of multiple phases. However, transient dynamics…

A stochastic process, when subject to resetting to its initial condition at a constant rate, generically reaches a non-equilibrium steady state. We study analytically how the steady state is approached in time and find an unusual relaxation…

Many psychological experiments have subjects repeat a task to gain the statistical precision required to test quantitative theories of psychological performance. In such experiments, time-on-task can have sizable effects on performance,…

In this paper, we wish to investigate the dynamics of information transfer in evolutionary dynamics. We use information theoretic tools to track how much information an evolving population has obtained and managed to retain about different…

Analysis of mathematical models in ecology and epidemiology often focuses on asymptotic dynamics, such as stable equilibria and periodic orbits. However, many systems exhibit long transient behaviors where certain aspects of the dynamics…

We define an opinion formation model of agents in a 1d ring, where the opinion of an agent evolves due to its interactions with close neighbors and due to its either positive or negative attitude toward the overall mood of all the other…

We study the intermittent fluorescence of a single molecule, jumping from the "light on" to the "light off" state, as a Poisson process modulated by a fluctuating environment. We show that the quasi-periodic and quasi-deterministic…

We develop a theory for transit times and mean ages for nonautonomous compartmental systems. Using the McKendrick-von F\"orster equation, we show that the mean ages of mass in a compartmental system satisfy a linear nonautonomous ordinary…